Beta is an indication of volatility and volatility is itself a variation in the price of stocks, or a stocks price fluctuation if you will. When examining beta value it is important to remember to compare it to other stocks in the same sector. Some sectors are naturally moving volatile than others.
Recession does cause panic among investors and therefore causes fluctuation which increase volatility. However since the beta value measured against the Dow Jones Industrial Average and the DOW is also in flux it is still a good over all indicator of how a stock is performing compared to others in its sector.
Increased amounts of individual investors and day traders with no real knowledge of the market have in my humble opinion made it more volatile. However a good stock is a good stock and those who know will recognize this and invest in it. Just remember to follow the fundamentals and stay diversified.